A cut-off tool of the general type with which the present invention is concerned is previously known from SE 8601533-6 (Publ. No. 452,713). In this prior-art tool, the individual V-groove in the insert, as well as the V-ridge on the tool part cooperating therewith, is designed with, at least theoretically, planar flank surfaces, the obtuse angle between the flank surfaces of the V-groove being about 140.degree. and the corresponding angle between the flank surfaces of the V-ridge on the tool part being about 130.degree.. Accordingly, the clearance angle between each flank surface of the V-ridge and the cooperating flank surface of the groove is about 5.degree., measured from the line along which the surfaces contact each other. In practice, the contact between the flank surfaces or flank sides of the groove and of the V-ridge is seldom a true line contact. After a varying period of use of the tool, the steel of the holder plate (which is considerably softer than the cemented carbide of the insert) allows, by plastic deformation, a certain "settling" of the insert relative to the flank sides of the V-ridge, such that a certain, in itself not adverse surface contact arises (however still only in the vicinity of the theoretical contact line). This surface contact presupposes that the insert on its cross-sectionally V-shaped underside is essentially straight in its longitudinal extent. In actual practice, however, this is not always the case. Thus, after compacting and sintering of the series-produced cemented carbide inserts, there may be considerable variation between, on the one hand, almost completely straight inserts (underside concavity less than 0.01 mm) to clearly concave inserts (concavity 0.05-0.08 mm). In the last-mentioned inserts, the flank surfaces of the V-groove almost completely lose contact with the corresponding flank surfaces of the V-ridge in its central area and surface or line contact is achieved only in the immediate vicinity of the two opposite ends of the insert. This is quite unsatisfactory, in that there is an imminent risk of chipping and crack formation in the insert.
To overcome the above-mentioned risk, it is conceivable per se to scrap all clearly concave inserts in the same way as is regularly done with inserts having convex undersides. However, the proportion of concave inserts in a series may be considerable, for which reason such scrapping would entail substantial economic losses.